Demystifying Domain and Range in iGCSE Maths 2025

Domain and range can seem a bit confusing at first, but they're actually quite straightforward once you understand the basics. This blog post will guide you through the key concepts, using examples and visuals to make it clear and simple.

What are domain and range?

Imagine a function as a machine that takes an input (x-value) and produces an output (y-value). The domain is simply the set of all possible input values that the machine can accept, while the range is the set of all possible output values that the machine can produce.

Visualizing domain and range

There are a few different ways to visualize domain and range:

• Mapping diagrams: These diagrams show the input values on the left and the output values on the right, with arrows connecting them to show how they are related.

• Graphs: On a graph, the domain is represented by the x-axis, and the range is represented by the y-axis.

• Tables of values: A table of values lists the input values and their corresponding output values.

How to find domain and range

The method for finding the domain and range depends on how the function is represented:

• Mapping diagram: Simply list the input values for the domain and the output values for the range.

• Graph:  Look for the minimum and maximum values on the x-axis for the domain and the minimum and maximum values on the y-axis for the range.

• Equation:  Analyze the equation to determine any restrictions on the input values (e.g., avoiding division by zero or taking the square root of a negative number). This will help you determine the domain. Then, consider the possible output values based on the function's behavior.

Exam-style questions

Here are a couple of examples of how domain and range questions might appear in your iGCSE Maths 2025 exam:

• Given a function and its domain, find the range. To solve this, substitute the values from the domain into the function to find the corresponding output values, which will form the range.

• Given a graph, determine the domain and range.  Visually inspect the graph to identify the minimum and maximum x-values for the domain and the minimum and maximum y-values for the range.

Tips and tricks

• Remember that the domain is always related to the x-values and the range is always related to the y-values.

• When working with graphs, draw vertical lines to visualize the domain and horizontal lines to visualize the range.

• Practice, practice, practice! The more you work with domain and range problems, the more comfortable you'll become.

By understanding these concepts and practicing exam-style questions, you'll be well-prepared to tackle domain and range in your iGCSE Maths 2025 exam. Good luck!